The invention relates to a method for determining the location-dependent impulse responses in the case of signal transmission from a transmitter in a transmission volume to a receiver in a reception volume, either the transmitter or the receiver being a device immobilized at a predetermined location and the other being a mobile device. The invention further relates to an apparatus designed for carrying out the method.
The impulse response is the output signal of a system that is excited using a Dirac impulse as input signal. For linear, time-invariant systems the impulse response is a quantity characterizing the system, which to determine is desirable for optimally designing the system.
In the case of complex real systems, the true impulse response can be an extremely complicated function of the time dependent on several parameters. Often it cannot be specified analytically or even be determined completely by measurement series. Rather its determination is restricted in view of a specific technical objective by measurements in parameter ranges that are relevant therefor.
In practice, considerable amounts of measurement data accumulate in the case of such measurements, and the impulse responses are normally not modeled until after the data collection by numerical measurement-data analyses. Here it is utilized that the impulse response H precisely describes the output signal A of the system for any pre-known input signal E over a convolution integral in the sense of a Green's function:A(t)=∫−∞∞H(t−t′)E(t′)dt′  (1)
If the output signal is measured at a location r while the input signal at the location r0 is predetermined, then it is also the impulse response that is a function of these locations, and the pair (r, r0) can be regarded as an index of a signal transmission channel.A(r,t)=∫−∞∞H(r,r0,t−t′)E(r0,t′)dt′  (2)
This applies in particular in the case of signal transmission by means of wave propagation, for example by means of sound or radio waves. The function H(r, r0, t) here takes into account all local circumstances that influence the wave propagation in a time-invariant manner, for example the existing arrangement of obstacles and reflectors in the scenery in which the transmitter and the receiver are located.
For experimentally determining the impulse response, usually a simplified measurement set-up is used that at the same time is a restriction to a modeling that has been shortened appropriately. The input signal is typically band-limited, i.e. the difference between the highest and lowest frequencies fmax and fmin, occurring in the signal is predetermined. Over and above this, transmitter and receiver are usually firmly immobilized at predetermined locations, i.e. individual selected channels are investigated.
This is for example convenient in acoustic applications where a listener sits opposite an arrangement of loudspeakers in an echo-free room and the sound signal reaching his ears is to be assessed. The sound channels are here influenced already by the presence of the head of the listener, and the transfer properties can be described by determining a so-called “head-related transfer function (HRTF)”.
A further example is the emission of a radio or cellular mobile signal from a firmly located transmission aerial. The question as to which frequency components of the transmission signal can be detected at the receiver at which quality in a pre-known terrain, for example inside a building, can be answered by measuring the “channel impulse response (CIR)”.
Knowing the impulse response then makes it possible to derive measures for changing it in a targeted manner, for example by changing reflecting surfaces in the scenery. For example, the reflectivity can be varied by means of suitable surface coatings.
A usual objective in the area of acoustic transmission is the avoidance of reverberation or echoes that result from the reflection of sound waves at the walls of a closed room, as sketched in FIG. 1. The receiver, a microphone (on the right in the picture), receives from different directions at markedly different times and with a different intensity a short sound impulse from the loudspeaker (to the left in the picture) on account of the finite speed of sound. This effect can have a very detrimental impact on the hearing pleasure in particular in concert halls where music is generated in a classically analogous manner. Here the aim will be, for the purpose of improvement, first of all to change the properties of the room in a targeted manner.
On the contrary, in the case of the digital playback of noise or music the reverberation can already be compensated for during the sound generation, knowing the acoustic room impulse response RIR. It has to be observed here that the room impulse response strongly depends on the location so that a compensation for a room point r1 is not valid for a neighboring room point r2. In realistic scenarios, in addition several sound sources will be often active simultaneously. Therefore a compensation has either to be carried out approximately for an entire volume and several, spatially distributed sound sources, or the position of the listener has to be detected continuously and the compensation has to be matched continuously to the location-dependent impulse response. For both compensation methods it is advantageous if the location-dependent room impulse responses from all sources to all locations in the relevant volume are known in advance. The continuous detection of the positions of the ears of the listener together with the previously detected information on the sound propagation from the sources into the volume then also permits a three-dimensional sound presentation on the basis of the principle of crosstalk cancellation.
Although the impulse response is a technically important quantity, until now it cannot be established for large room volumes—i.e. for a very large number of channels—at justifiable efforts. You rather have to rely on an assessment on a random basis in such a way that for assessing the acoustics of an auditorium—indicated by the boundary in FIG. 1—the microphone is brought to a plurality of locations inside a reception volume intended for the auditorium—indicated by the cube in FIG. 1 —, in each case the impulse response is determined locally and then also statements on room points situated away from the measurement points are calculated by interpolation.
For a reliable interpolation, the Nyquist-Shannon sampling theorem has to be observed here, i.e. the distances of the measurement points in the room, Δ, and during the time, Δt, have to satisfy the Nyquist criterion (mentioned here for fmin=0):
                              Δ          ⁢                                          ⁢          t                ≤                              1                          2              ⁢                                                          ⁢                              f                max                                              ⁢                                          ⁢          with          ⁢                                          ⁢          Δ                ≤                  c                      2            ⁢                                                  ⁢                          f              max                                                          (        3        )            
Here c is the speed of sound in the air, approximately 330 m/s, and fmax can be assumed to be limited to approximately 20 kHz for the human hearing. This results in Δ≤8.25 mm as a requirement as to the maximum distance of the supporting points in local coordinates for completely determining the impulse responses in a reception volume that can easily amount to several 100 cubic meters for example in the case of an auditorium. According to this, while maintaining fmax=20 kHz, the impulse response would have to be determined at approximately 1.78 million supporting points for each cubic meter so as to reliably interpolate it to the entire volume. In the case of a reduction of fmax, the number of supporting points can be lowered correspondingly, but for many practically relevant cases it will continue to be very high. Even in the case of a restriction to fmax=4 kHz (telephone bandwidth), approximately 14,250 supporting points per cubic meter are still necessary.
If the determination of the room impulse responses is to be carried out within a reasonable time, at first it could be imagined to bring a correspondingly tightly packed arrangement of microphones into the reception room, as sketched in FIG. 2. But even without thinking about the material and labor costs necessary for this, it is immediately clear from FIG. 2 that so many physically real microphones would massively interfere with the sound field already as a result of their presence, what makes the meaningfulness of this procedure doubtful.
A second approach to determining the volume can be seen in determining the impulse response without subsequent model analysis, but rather in real-time at each position of the receiver and thereby to aim at accelerating the data acquisition and a fast movable measurement device. An apparatus intended for this purpose for determining the room-acoustic impulse response can be gathered from DE 10 2007 031 677 A1. Here paragraph 0041 reads: “In contrast to known static one-time measurements, the evaluation takes place dynamically in real time, i.e., even if the acoustic measurement device is moved the change in the room-acoustic impulse response or a complex transfer function such as quantity or signal strength and phase are indicated immediately.” This suggests that the microphone might be moved along any trajectory through the room while recording the measurement values and then one might instantaneously receive the looked-for impulse response at each point of the trajectory. In fact, the impulse response has a minimum temporal length as a function of the emitted frequency band, and it can be detected completely in the sense of the measurement task only if the microphone remains at a location at least for this time span. What the printed publication therefore suggests here is a channel change during the current measurement of the channel properties, the person skilled in the art in general and does not expect any reliable statements therefrom.
This approach can still be pursued further. However, an implementation requires suitable measures so as to somehow obtain the missing information from the actually detected measurement data. Anyhow, DE 10 2007 031 677 A1 does not show such measures.
In contrast thereto, the doctoral thesis by Ajdler “The Plenacoustic Function and its Applications”, Thesis No. 3653, École Polytechnique Fédérale de Lausanne, 2006, deals in particular in chapter 5 with the dynamic measurement of the acoustic RIR by means of transmitters or receivers moved during the measurement and also with measures for reconstructing the RIR. On the basis of general statements on the power density spectrum of the location and time-dependent sound pressure field (the so-called “plenacoustic function”) and taking into account the Doppler effect in the frequency analysis of the measured output signal, a method is suggested there so as to draw conclusions as to the RIR at any locations on the trajectory from the measurement data detected along a trajectory.
The implementation of Ajdler's method requires that the trajectory is either a straight line or a circular arc. In chapter 6 of his work, Ajdler only touches upon randomly running trajectories, but it can simply be gathered that the transferability of the solution approach to such trajectories is not excluded; a concrete implementation suggestion is missing. For implementation, it is further demanded that either the transmitter or the receiver is moved along the predetermined trajectory at a constant speed and that the acoustic input signal exhibits predetermined frequency-band gaps that are closed during the measurement of the output signal by the Doppler effect. These requirements demand a precision of robot arms or comparable drivable apparatus for traversing the predetermined trajectory. The reconstruction of the RIR according to Ajdler in large rooms—and there simply also only for locations on the trajectory—would be accompanied by a considerable measurement effort and high costs in terms of apparatus and is therefore no realistic option.
The present description is about modeling the function H(r, r0, t). It not only represents a single impulse response but a diversity of impulse responses for an arbitrarily dense continuum of position vectors. To illustrate this, with reference to H(r, r0, t) there are mentioned below also in a shortened manner “location-dependent impulse responses” (plural), even though only one function is meant.
Until today, the prior art does not know any method for determining the location-dependent impulse responses for the signal transmission via wave propagation in a volume, that is based on measurement data that are detected along a trajectory that runs inside the volume in an arbitrary manner. On the one hand, such a method has to permit that the trajectory is traversed with imprecise and therefore inexpensive means. On the other hand, statements on any locations of the volume must be possible after the analysis of a measurement that can be carried out inside an acceptable time and cost-effectively.